The USDA's NCRS service has a calculation for raising cattle, which comes to about 20 acres (8 hectares) for 11 beef cattle. 5 million cattle would require about 9.1 million acres (3.6 million hectares). That's one day's consumption. A year would require 365 times that = 1.825 billion cattle. An average beef cow will require about 0.21% of their bodyweight's worth of average quality forage (from http://beef.unl.edu/cattleproduction/forageconsumed-day).
Most cows give birth to a single calf - from http://www.dairymoos.com/how-many-babies-do-cows-have/, so taking just the yearlings would keep the cattle population steady. Cows can manage about 330-340 days between births (from http://beef.unl.edu/pregnantcows), so as we're emphasising that the animals should be of quality, I will assume that we allow a year between births in order to improve the breeding stock (and to simplify calculations). (A yearling cow would weigh about 1100lb/500kg, so somewhat higher than the 200kg specification in the question.)
To maintain a steady supply under these circumstances, we would need about 365x9.1 million = 3.32 billion acres or 1.344 billion hectares for the cows, and roughly about the same again for the calves, yielding a total of about 6.64 billion acres/2.7 billion hectares/27 million square kilometres. (For comparison, Africa is about 30 million square kilometres, and North America is about 24 million square kilometres.) It seems infeasible to use cattle as the large animals.
Mature male red deer weigh up to 240kg in weight, so they may be suitable replacements (and are probably closer to the OP's cultural requirements). Red deer hinds produce about 1 calf per year, with dominant males holding up to 20 hinds in their harem, so we can assume there is a 5% "male overhead".
Farmed red deer reach 200kg weight after about 5 years (from http://www.tandfonline.com/doi/pdf/10.1080/00288233.1988.10423417), so in order to be able to harvest 5 million individuals per day, we would need to maintain a population of 5*365*5 million = 6.625 billion animals plus the breeding stock of 365*5 million*1.2 = 2.19 billion animals, for a total of 8.815 billion animals. We should allow up to 12 animals per hectare of arable lowland pasture (source http://deerfarmdemoproject.scottish-venison.info/wp-content/uploads/2016/04/starter-guide-deer-farming-park-management.pdf), so we would need 735 million hectares (=7.35 million square kilometres). For comparison, Australia is about 7.7 million square kilometres. This is obviously better than the cattle situation, but still a very large amount of land. The pasture will support the deer as long as it remains productive (e.g. not in winter for the higher latitudes).
Obviously, I have no information on giant birds weighing 200kg; the ostrich tops out at about 154kg for a mature male. If we take that as the example, we can stock 100 yearling birds per hectare (from http://www.publish.csiro.au/ebook/download/pdf/3526, asssuming high rainfall or irrigation), and each yearling would weigh about 70kg (extrapolated from the numbers in http://world-ostrich.org/profitable-slaughter-age-in-ostrich/), meaning that we would need about 14.3 million birds to satisfy one day's consumption of large animals. An average female ostrich will lay about 45-50 eggs/year (from https://www.ostriches.org/about-ostrich/faqs), so you would need about 97.24 million laying females to lay a sufficient quantity of eggs to satisfy a constant consumption. This results in a requirement for space for 340*14.3 million birds/100 birds-per-hectare = 48.6 million hectares for the juveniles, and 97.24 million/24 birds-per-hectare = 4 million hectares for a total of 52.6 million hectares (=526,000 square kilometres).
So, farming ostriches is much more space-efficient than cattle or red deer. You could do similar calculations for pigs, sheep, etc. probably with intermediate results.
In terms of the 100 million smaller (10kg mass) animals, I'm not sure what animals would weigh about 10kg (coypu?), but if we assume you meant animals like chickens (which typically weigh about 2kg at slaughter for broiler chickens), then that would mean 500 million chickens per day (or 182.5 billion chickens/year). Some breeds can lay up to 300 eggs/year, so if we assume that, that means a population of about 567 million broiler breeder hens.
As we're interested in having producing decent-looking chickens, we will assume free-range farming methods. Each chicken will need about 3 square feet (0.28 square metres) of space to roost and 15 square feet/1.39 square metres of space for ranging, for a total of 18 square feet/1.67 square metres (source http://www.thehappychickencoop.com/how-much-room-do-chickens-need/). In addition, the chickens will take longer to reach slaughter weight - typically about 56 days instead of 42 days (source http://www.fwi.co.uk/poultry/free-range-chicken-meets-the-challenges.htm) - so we would need to maintain a juvenile population of about 56*500 million = 28 billion juveniles. So, 28 billion juveniles and 567 million adults will require 47.7 billion square metres = 4.77 million hectares = 47,707 square kilometres.
Broiler chickens need about 7lb (3.2kg) feed in their lifetime (averaging about 20% animal or vegetable protein and 80% grains and alfalfa/fresh pasture, taken from http://animalsciencey.ucdavis.edu/avian/feedingchickens.pdf). Wheat is produced in the US at a yield of 7600kg/hectare/year, so each hectare of wheat will support nearly 3000 chickens. We would need about 10 million hectares (= 100,000 square kilometres) of wheat to support the chickens.
For comparison, the US slaughters 33.2 million cattle and 8.6 billion chickens a year annually, so your city requires about 55 times more cattle and 22 times more chickens than the entire US (though the US does consume other meats as well).
(1 hectare is the area of a square of 100 metres per side; there are 2.47 acres/hectare, 100 hectares/square kilometre and 259 hectares/square mile.)
Delivery in a decent condition
This would rqeuire a planned farm and city layout, with farms arranged around a network of spoke-and-hub train networks outside the city, mirrored by a spoke-and-hub network within the city.
The farms will be continually channelling animals from large holding pens onto modular animal cars at the local hubs, hitched to train engines. These trains would take the cars to regional hubs where they would be unhitched and replaced by empty cars. They would then head back to their regional hubs to repeat the process.
Meanwhile, the loaded cars would be hitched to long trains to take the animals into the city in a near-continuous stream of trains. These trains would unhitch their loaded carriages at district hubs in the city, and hitch up with empty cars (or cars taking animal carcasses/waste) back out to the termini where the cars would be unhitched to be emptied and washed. The trains would then pick up empty clean cars and head back to the district hubs where they would repeat the cycle.
The district hubs in the city would hitch the loaded cars onto a number of local trains, to transport them to neighbourhood hubs, where they would be unloaded into large pens for the consumer to obtain. The empty cars would be taken back to the district hubs, thus completing the loop.
You would need to transport 5 million large and 100 million small animals (or 500 million chickens) a day, so if we assume that the rural network consists of 20 regional hubs, each linked to 20 local hubs, that means that each of the 400 local hubs would need to handle 12,500 large and 250,000 small animals/1,250,000 chickens a day. If we assume that each of the modular cars can take 40 cattle (from http://www.fwi.co.uk/poultry/free-range-chicken-meets-the-challenges.htm, assuming that each cow weighs about half a short ton). Say we allocate about 300 square cm area and 50cm height, including ventilation, per chicken in the modular boxcar, packaged in 12-chicken crates. For a boxcar with an internal space of 20m x 3m x 3m high, this yields a capacity of 12,000 chickens per boxcar. Each of the 400 local hubs would need 313 boxcars-journeys/day for the cattle and 105 boxcar-journeys/day for the chickens for a total of 418 boxcar-journeys/day. The regional hubs would aggregate these into 8360 boxcar-journeys/day into their corresponding district hubs in the city.
If we assume that the regional trains have up to about 4000m of cars (the Canadian National Railway regularly runs trains that are 4200m in length), which for cars of 22.5m external length (20m internal length) means that each train has 178 cars, which we'll round up to 180 cars for ease of calculation (corresponding to 20 local rural trains of 9 cars). Each regional hub would then need to send 47 trains a day into the city, or 2 trains an hour around the clock.
At the district hubs, these trains would be split back into shorter segments, corresponding to the original rural local trains, and despatched to the neighbourhood hubs, where they would be unpacked.
If we assume that, with sufficient manpower, each cattle car could be unloaded in 5 minutes, and each poultry car would require about an hour to unload the 1000 crates of chickens, it means that we would be unloading 2 trains at any one time, whilst reassembling a newly-emptied third train. This means we would need at least 3x9x22.5m = ~610m of freight sidings at the city neighbourhood hubs.
The neighbourhood hubs would have to handle the same amount of animals as the rural local hubs (12,500 large animals and 250,000 small animals or 1,250,000 chickens) on a daily basis, so will need paddocks and poultry sheds and personnel to store and look after these animals whilst waiting to be collected by the city population.
It is just about feasible, assuming that the city has a huge dedicated farming and transport infrastructure around it to support its huge food intake. It would require a vast area though, to support the huge numbers of animals; if we consider a equivalent situation on Earth, it would be something like a city in the middle of Africa (or Australia, if using red deer) supported by the whole of the continent, assuming that all of Africa was average-or-better quality pasture. Whether this is feasible in your setting is up to you.